Need advice on bizarre accidental problem

[Brace]

I just went to my school's testing center to test into the class I needed to take in order to fulfill the requirements to take the class I actually need to take the semester afterward. However, I tested so well that I could now go straight into that class if I wanted to. Concerns with this:

1. Even if I did get them all correct, it took me about an hour to answer the 14 questions in the test. This is not pop-quiz speed. Furthermore, I feel that to a large extent I was only able to answer many of them because they were multiple choice, and I literally guessed on a couple based on process of elimination and then staring at the remaining answers really hard, pretending I saw a pattern, and choosing based on that.

1a. Even if I am still able to make use of this dubious set of skills to get through College Algebra, I still wouldn't really be learning the material, and I plan on going into Engineering so it would probably be really good for me to learn the material.

2. But if I took College Algebra this summer, I could jump into Trig or Calc or w/e in the fall, basically cutting an entire extra semester out of my overall long term academic future.

3. Alternatively I could just take the entire goddamn summer off for work.

4. Taking the extra class to drill everything into me wouldn't cost me anything except time and money really, but then I would be taking College Algebra alongside two other classes. If I took it now, I would be taking it in an 8 week excessively fast class, but it would be the only class I would be taking.

5. wtf guys technically I could take both classes at the same time and actually (I think) qualify for financial aid due to this, but then I'd be in extra debt. But then I'd be able to pay off my motorcycle, and it's looking like I won't be able to finish College without taking out private loans in addition to the federal loans anyway.

6. firstworldproblems

7. seriously though, wtf should I do


tl;dr I tested into College Algebra when I only intended to test into Intermediate Algebra, and don't know if my math is good enough to go straight into College Algebra.

[Yesila]

If you're worried that you lucked into passing the test trying taking it again, or take a different but similar test.

This http://www.math.unt.edu/mathlab/emathlab/review%20test%20%28college%20algebra%29.htm was the first google hit when I went looking for an additional test for you. Try it. See if you do just as well on this one. If so maybe you are indeed ready... if not then maybe it was just lucky guessing.

Fast paced summer versions of full semester classes are often hard and students sometimes leave them with a lower level of understanding then if they had taken the full semester version. So taking a class that you are barely qualified to take could be disastrous for your self-esteem, gpa and future courses... Then again motivated students that have (and are willing to put in) the extra homework time (that a faced paced class requires) can do well.

Taking an intermediate Algebra (which your placement score says you don't even need) class over summer might server to hone your skills and make you feel more prepared for a fall version of college algebra... then again since you already qualify for college algebra you could achieve the same thing by doing a self study of intermediate algebra topics to better prepare you for when you do take the college algebra class. http://www.khanacademy.org/exercisedashboard is a (free) site that has many practice problems and mini-video lectures on topics that could be an asset to help with self study. Of course there are other similar sites, as well as the old-school option of checking out a intermediate algebra book from the library in order to help with self study.

Good luck on deciding what to do, if your nervous about being ready for college algebra defiantly take that test or a similar one again to give you some additional confirmation that you are ready, or an indication that maybe you aren't.

[Qaanol]

I strongly recommend jumping ahead as far as possible. You can pick up a used textbook or scope out the Khan academy to brush up on anything you missed. The worst that’ll happen is you’ll realize a few weeks into the advanced course that you need to switch down a level, and do so. But if you don’t at least try to start at an advanced level, there’s a good chance you’ll always be a semester or more behind where you could have been, and your courses will be quite boring.

The rules of algebra are pretty intuitive once you understand that it’s just arithmetic with letters. Most of the time you’ll start off with two things equal to each other, and you want to do the same things to both sides so they stay equal while you rearrange terms. You definitely want to learn trigonometry and calculus for engineering.

They are also pretty straightforward at least conceptually. The trig functions sine, cosine, and tangent are just ratios of the side-lengths of right-angled triangles. As in, measure one side of the triangle, measure another side, and divide one value by the other. All the rest of it is just uses of the Pythagorean theorem and rules for similar triangles.

Calculus is at heart the study of limits, but from a practical standpoint it just tells you how to calculate rates of change (the derivative) and accumulated totals (the integral). There are a few basic things that get proved, like the derivatives of polynomials, trig functions, exponentials, and the chain rule, and the idea that the derivative “undoes” the integral (in the sense of being inverse operations). After that you almost never have to touch limits again, at least not for engineering.

[Brace]

I guess I forgot to mention that I'm not allowed to drop or fail classes due to taking an excess of credits and triggering a financial aid probation as a result.

[Qaanol]

I guess I forgot to mention that I'm not allowed to drop or fail classes due to taking an excess of credits and triggering a financial aid probation as a result.

Surely you could switch from one class to another though, if the profs signed off on it?

[gorcee]

I guess I forgot to mention that I'm not allowed to drop or fail classes due to taking an excess of credits and triggering a financial aid probation as a result.

Surely you could switch from one class to another though, if the profs signed off on it?

Yeah, this is where you consult with the departmental folks and an adviser/counselor.

[Ben-oni]

Aah, skipping ahead. It's a difficult question, and in the end, everyone needs to find their own answer. But there are issues to consider.

1) Will you actually go out of your way to learn/review material that isn't required for a course? Will you actually go online and read up on the material you skip? When you hear about a new concept, will you google it?
2) Does mathematical understanding come naturally to you? That is, can you correctly apply a principle after only hearing about it once?
3) Which engineering discipline are you going into? If it's EE, you need to be going into calculus now. If ME, you should be starting with trig. Being behind with math can be a detrimental delay to any engineer: you can't take various engineering courses until you've finished a certain level of math, which means earlier semesters are packed with generals, and the final semesters are packed with too many difficult engineering courses. Or you could go in for the five year plan, but if you do that, you should plan it from the start.

If you answered either "Yes" to he first two questions, or "EE" for the second, then go for the more advanced course.

[eSOANEM]

As another way of looking at it, in my experience, the best way to improve your skills at a given type of maths (given a certain basic level of competence) is not to do more problems at that level, but rather to push on and do some harder maths because then, in retrospect, it will all seem so much easier.

As an example, the best way to get good at algebra is, in my experience, doing various problems at a higher level which require algebra in their solutions (this being almost any problem) so, for example, doing trig or calculus will improve your algebra no end and, once you get onto calculus, the best way to improve your skills at applying the standard derivatives is not to do them over and over again until you've learnt them by rote, but rather to apply them to cases requiring the chain rule or product rule etc.

As a more personal example, I am terrible at remembering facts. As such, when I had to learn the compound angle formulae for trig, it was horrible. Now that they're being used more incidentally in calculus, I'm finally learning them.

[PM 2Ring]

As a more personal example, I am terrible at remembering facts. As such, when I had to learn the compound angle formulae for trig, it was horrible. Now that they're being used more incidentally in calculus, I'm finally learning them.

Yeah, it's easy to mix the signs up on those compound angle formulae. FWIW, I find it easiest to remember them via complex numbers.
Let C = A + B
cos(C) + i sin(C) = (cos(A) + i sin(A)) * (cos(B) + i sin(B))
Therefore,
cos(C) = cos(A)cos(B) - sin(A)sin(B)
sin(C) = cos(A)sin(B) + sin(A)cos(B)

[undecim]

I strongly recommend jumping ahead as far as possible. You can pick up a used textbook or scope out the Khan academy to brush up on anything you missed. The worst that’ll happen is you’ll realize a few weeks into the advanced course that you need to switch down a level, and do so. But if you don’t at least try to start at an advanced level, there’s a good chance you’ll always be a semester or more behind where you could have been, and your courses will be quite boring.

This.

[eSOANEM]

As a more personal example, I am terrible at remembering facts. As such, when I had to learn the compound angle formulae for trig, it was horrible. Now that they're being used more incidentally in calculus, I'm finally learning them.

Yeah, it's easy to mix the signs up on those compound angle formulae. FWIW, I find it easiest to remember them via complex numbers.
Let C = A + B
cos(C) + i sin(C) = (cos(A) + i sin(A)) * (cos(B) + i sin(B))
Therefore,
cos(C) = cos(A)cos(B) - sin(A)sin(B)
sin(C) = cos(A)sin(B) + sin(A)cos(B)

Yeah, the main one I have trouble with is that I get cos(C) as its negative although it's fairly simple to check which of those it is by checking the value when both of the angles are 0.

Also, the tan one is a pain although this is mainly because I think of it as being related to the relativistic velocity addition formula (which is the hyperbolic version), but forget to change the sign of tan(A)tan(B) on the bottom.

[PM 2Ring]

Yeah, the main one I have trouble with is that I get cos(C) as its negative although it's fairly simple to check which of those it is by checking the value when both of the angles are 0.

That was my strategy, before I learned about complex numbers.

Also, the tan one is a pain although this is mainly because I think of it as being related to the relativistic velocity addition formula (which is the hyperbolic version), but forget to change the sign of tan(A)tan(B) on the bottom.

Fair enough; the tan sum formula is burned into my brain from spending far too much time playing with arc-cotangents of integers while looking for Machin-like formulae for pi. Although there are more modern ways of calculating pi, the Machin-like formulae are still popular, and they're the most practical way if you're crazy enough to want to do it by hand - about a decade ago I used pi/4 = arctan(1) = 8*arctan(1/10) - arctan(1/239) - 4*arctan(1/515) to calculate pi to around 10 digits, just using pencil & paper.

FWIW, I just found this site dedicated to computing pi via arc-cotangents a few weeks ago.

[Meem1029]

FWIW, I find it easiest to remember them via complex numbers.
Let C = A + B
cos(C) + i sin(C) = (cos(A) + i sin(A)) * (cos(B) + i sin(B))
Therefore,
cos(C) = cos(A)cos(B) - sin(A)sin(B)
sin(C) = cos(A)sin(B) + sin(A)cos(B)

I hadn't seen that before. I've seen the basic DeMoivre's theorem (or however you spell that, it's 2 in the morning so I'm not really sure) approach to double angle, etc. formulae, but not this. It's awesome and will be of much help!

[MisterH]

I don't know a single sucessful person that got where they are without getting a lucky break or having taken a risk.

Obviously the one thing that is consistent is they put in the effort for whatever they are doing and they are infinitely committed to their ultimate goal!

Your fear is quite natural but it is your friend - it is your subconscious and perception preparing you for the hazards that lie ahead. You have already acknowledged this and appear to be preparing yourself for the challenge ahead. You don't need us to tell you what to do - you already know the answer. The fact that you are aware of your weaknesses is also a strength and you can use this to your advantage - either by avoiding situations where you would fall foul of them, or formulating strategies to overcome them.

I imagine you felt excited when you aced the test and then a little guilty for your approach, however it appears to me that you applied some Maths in your strategy - you say you were looking for patterns and took a chance - that's statistical analysis and probability in action my friend.

You seem like a friendly, good to know kind of person, so my advice would be to use your analysis skills to find someone with equal or slightly better ability than you on the first couple of days and team up with them. It is always easier to learn something when you have someone else to kick it around with and as a bonus you will have a new nerdy pal!

Good luck! GO FOR IT.